The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. The techniques available in the literature to accurately estimate these uncertainties typically only work in an ...

We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions ......

We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system ...

We revisit the concept of source term representation, originally developed for boundary control problems subject to pointwise state constraints in the domain, and apply it to linear-quadratic parabolic control problems ...

Most high-dimensional real-life data exhibit some dependencies such that data points do not populate the whole data space but lie approximately on a lower-dimensional manifold. A major problem in many data mining applications ...

We prove first- and second-order optimality conditions for sparse, purely time-dependent optimal control problems governed by a quasilinear parabolic PDE. In particular, we analyze sparsity patterns of the optimal controls ...

We perform 3D incompressible two-phase flow simulations of rising droplets. Based on a similar 2D benchmark, a 3D benchmark configuration with two test cases is formulated in which we compare the flow solvers DROPS, NaSt3DGPF ...

On the example of the simplest C⁰ spline quarklet construction of [1], we demonstrate the possible reduction of the complexity estimates for the approximation of singularity functions on the unit interval given ......

This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution-free ......

In this article we rigorously show consistency of generalized cross-validation applied to an exemplary ill-posed integral equation, given a finite number of noisy point evaluations. In particular, we present non-asymptotic ...